What is a40 for the arithmetic sequence presented in the table below?

n 8 12

an 60 48

Hint: an = a1 + d (n - 1), where a1 is the first term and d is the common difference

Lets first get the common difference = d.

Using,

an = a1 + d (n-1)

a8 = a1 + d (8-1)

60 = a1+7d

a12 = a1 + d (12-1)

48 = a1 + 11d

from these 2 equations we will get a1, d

subtracting them, we get

60-48 = 7d-11d = - 4d

12 = - 4d

d = - 3.

and

60 = a1 + 7d = a1 + 7 (-3) = a1 - 21

a1 = 60+21 = 81.

now a40 = a1 + d (40-1) = 81 + (-3) 39

a40 = - 36.